Gooseberry bush baby plants?

Hi All,

Wonder if you can help me, I have a well growing gooseberry bush with lots of fruit on it, but underneath it are lots of small plants which are very similar. These are very tiny plants but are spiny, and look similar to the bush.

Would these be baby plants, and if so, how do I deal with them? Sorry to sound so dense, but my gardening knowledge is very limited, but growing .

Any advice would be much appreciated.

soaplady